How many perfect cubes are there from 1 to 500? How many are perfect square among cubes?

Find the cubes of 10, 30 , 100, 1000. What can you say about the zeros at the end?

Solution:

103 = 1000

303 = 27000

1003 = 1000000

10003 = 10000000000

The number of zero of a cube are 3 times, the no. of zero of numbers

What are the digits in the unit’s place of the cubes 1, 2, 3, 4, 5, 6, 7, 8 , 9, 10? Is it possible to say that a number is not a perfect cube by looking at the digit in unit’s place of the given number, just like you did for squares?

Solution:

a

a3

digit in the units place

1

1

1

2

8

8

3

27

7

4

64

4

5

125

5

6

216

6

7

343

3

8

512

2

9

729

9

10

1000

0

No, its not possible to tell a number is not a perfect cube by looking at the digit in unit’s place of the given number.